Palindrome Partitioning DP Minimum Cuts in DSA Typescript - Execution Trace

Concept Flow - Palindrome Partitioning DP Minimum Cuts

Start with full string

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Check all substrings palindrome?

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If substring is palindrome

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No cut needed for this substring

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Else try all cuts

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Calculate min cuts using DP

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Store min cuts for substring

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Move to next substring

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Repeat until full string processed

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Return min cuts for full string

We check all substrings to find palindromes, then use dynamic programming to find the minimum cuts needed to partition the string into palindromes.

Execution Sample

DSA Typescript

const minCut = (s: string): number => {
  const n = s.length;
  const dp = Array(n).fill(0);
  const palindrome = Array.from({ length: n }, () => Array(n).fill(false));
  for (let end = 0; end < n; end++) {
    let minCuts = end;
    for (let start = 0; start <= end; start++) {
      if (s[start] === s[end] && (end - start < 2 || palindrome[start + 1][end - 1])) {
        palindrome[start][end] = true;
        minCuts = start === 0 ? 0 : Math.min(minCuts, dp[start - 1] + 1);
      }
    }
    dp[end] = minCuts;
  }
  return dp[n - 1];
};

This code finds the minimum cuts needed to partition the string into palindromes using dynamic programming.

Execution Table

Step	Operation	Substring Checked	Palindrome?	dp Array State	minCuts	Visual State
1	Check substring s[0..0]	"a"	True	[0, _, _, _, _]	0	"a" is palindrome, dp[0]=0
2	Check substring s[0..1]	"ab"	False	[0, 1, _, _, _]	1	"ab" not palindrome, dp[1]=1
3	Check substring s[1..1]	"b"	True	[0, 1, _, _, _]	1	"b" palindrome, dp[1]=min(1, dp[0]+1=1) =1
4	Check substring s[0..2]	"aba"	True	[0, 1, 0, _, _]	0	"aba" palindrome, dp[2]=0
5	Check substring s[1..2]	"ba"	False	[0, 1, 0, _, _]	1	"ba" not palindrome
6	Check substring s[2..2]	"a"	True	[0, 1, 0, _, _]	0	"a" palindrome
7	Check substring s[0..3]	"abac"	False	[0, 1, 0, 1, _]	1	"abac" not palindrome, dp[3]=min(3, dp[2]+1=1) =1
8	Check substring s[1..3]	"bac"	False	[0, 1, 0, 1, _]	2	"bac" not palindrome
9	Check substring s[2..3]	"ac"	False	[0, 1, 0, 1, _]	2	"ac" not palindrome
10	Check substring s[3..3]	"c"	True	[0, 1, 0, 1, _]	1	"c" palindrome
11	Check substring s[0..4]	"abacd"	False	[0, 1, 0, 1, 2]	2	"abacd" not palindrome, dp[4]=min(4, dp[3]+1=2) =2
12	Check substring s[1..4]	"bacd"	False	[0, 1, 0, 1, 2]	3	"bacd" not palindrome
13	Check substring s[2..4]	"acd"	False	[0, 1, 0, 1, 2]	3	"acd" not palindrome
14	Check substring s[3..4]	"cd"	False	[0, 1, 0, 1, 2]	3	"cd" not palindrome
15	Check substring s[4..4]	"d"	True	[0, 1, 0, 1, 2]	2	"d" palindrome
16	End	-	-	[0, 1, 0, 1, 2]	-	Minimum cuts for full string is dp[n-1]=2

💡 All substrings checked, dp array filled, minimum cuts found at dp[n-1]

Variable Tracker

Variable	Start	After Step 1	After Step 4	After Step 7	After Step 11	Final
dp	[_, _, _, _, _]	[0, _, _, _, _]	[0, 1, 0, _, _]	[0, 1, 0, 1, _]	[0, 1, 0, 1, 2]	[0, 1, 0, 1, 2]
palindrome	All false	palindrome[0][0]=true	palindrome[0][2]=true	palindrome[0][2]=true, palindrome[3][3]=true	palindrome[4][4]=true	palindrome matrix updated accordingly
minCuts	n/a	0	0	1	2	2

Key Moments - 3 Insights

Why do we set minCuts to 'start === 0 ? 0 : dp[start - 1] + 1' when a palindrome substring is found?

Because if the palindrome substring starts at index 0, no cuts are needed before it (minCuts=0). Otherwise, we add 1 cut after the previous substring's minimum cuts (dp[start - 1] + 1). See execution_table rows 4 and 7.

Why do we check 'end - start < 2 || palindrome[start + 1][end - 1]' to confirm a palindrome?

Because substrings of length 1 or 2 are palindrome if characters match. For longer substrings, the inner substring must also be palindrome. This ensures correct palindrome detection. See execution_table rows 1 and 4.

Why does dp[end] store the minimum cuts needed for substring s[0..end]?

dp[end] accumulates the minimum cuts needed to partition the substring from start to end into palindromes. It updates as we find better partitions. See variable_tracker dp values and execution_table dp Array State.

Visual Quiz - 3 Questions

Look at the execution_table at Step 4, what is the value of dp[2] after checking substring "aba"?

A 1

B 2

C 0

D 3

💡 Hint

Check the dp Array State column at Step 4 in execution_table

At which step does the dp array first get the value 1 for any index?

A Step 2

B Step 7

C Step 1

D Step 11

💡 Hint

Look at dp Array State column in execution_table rows 1 and 2

If the input string was "aaaa", how would the dp array change compared to the current execution?

A dp would increase by 1 at each step

B dp would be all zeros because every substring is palindrome

C dp would be the same as current

D dp would be all ones

💡 Hint

Consider palindrome substrings and dp updates in variable_tracker and execution_table

Concept Snapshot

Palindrome Partitioning Minimum Cuts:
- Use DP array dp[n], dp[i] = min cuts for s[0..i]
- Use palindrome table to check substrings
- If s[start..end] palindrome, dp[end] = min(dp[end], dp[start-1]+1)
- If palindrome starts at 0, dp[end] = 0
- Result is dp[n-1]

Full Transcript

This visualization shows how to find the minimum cuts needed to partition a string into palindromes using dynamic programming. We check every substring to see if it is a palindrome using a 2D boolean table. For each end index, we try all start indices to find palindrome substrings. If a substring is palindrome, we update the dp array with the minimum cuts needed. The dp array stores the minimum cuts needed for the substring from the start to the current end index. The final answer is dp[n-1]. The execution table traces each substring check, palindrome detection, dp updates, and the visual state of the dp array. The variable tracker shows how dp and palindrome tables change over time. Key moments clarify why we add cuts only after previous partitions and how palindrome checks work. The quiz tests understanding of dp values and palindrome logic. This method efficiently computes minimum palindrome partition cuts.